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Blizzard [7]
3 years ago
10

Find the value of x, rounded to the nearest tenth.

Mathematics
1 answer:
german3 years ago
7 0

Answer:

25.8

Step-by-step explanation:

We use the segment of secants theorem to find x. The theorem states that the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. That means (a+b)b=(c+d)d. Then we simply plug in the numbers: (x+5)5=(15+7)7. Then solve for x by simplifying (x+5)5= 154, divide by 5 on both sides, x+5= 30.8, and subtract 5 from both sides, x= 25.8.

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Answer:

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Step-by-step explanation:

<u>Explanation</u> :-

The area of triangle( A) = \frac{1}{2} base X height    ..........(1)

Let 'b' be the base and 'l' be the length of the triangle

The base of a triangle is shrinking( means decreasing) at a rate of 11 cm/s

that is \frac{db}{dt} = -11cm/sec

The height of a triangle is increasing at a rate of 11 cm/s

that is \frac{dh}{dt} = 11cm/sec

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applying uv formula  \frac{d(uv)}{dx} = u( \frac{dv}{dx}) + v(\frac{du}{dx} )

Differentiating equation (1) with respective to 't'

\frac{dA}{dt} =\frac{1}{2}  ( b(\frac{dh}{dt} )+h ( \frac{db}{dt}))

substitute all values in above equation, we get

h= 10cm , b = 8cm , \frac{db}{dt} = -11cm/sec and \frac{dh}{dt} = 11cm/sec

 \frac{dA}{dt} = 10 (-11) + 8(11 )

After simplification , we get

\frac{dA}{dt} =\frac{1}{2}  (-110 +88) = -11 cm^2 /sec

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